Devices and methods for light control in material composites

ABSTRACT

Grating structures adapted to support cavity modes (“CMs”), including CMs produced by waveguide modes (WGs) of TE-polarized radiation; and those produced by WGs or vertically-oriented surface plasmons (VSPs) on the groove walls of incident TM-polarized radiation are provided. Such grating structures include those that provide enhanced transmission for a predetermined polarization state at a predetermined wavelength, simultaneous TM and TE transmission, and those that provide light circulation and weaving. The grating structures can include wires, or arrays of holes in thin (metallic) films, and include multiple-groove-per-period structures. Methods for optimizing such grating structures are also provided.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. provisional application Ser. No. 60/874,037, filed Dec. 8, 2006, the entirety of which is incorporated herein by reference.

GOVERNMENT RIGHTS

The U.S. Government may have certain rights in this invention including the right in limited circumstances to require the patent owner to license others on reasonable terms as provided for by the terms of a Phase I Small Business Innovative Research (SBIR) Contract No. 0539541, entitled “Advanced Silicon-based Photodetectors Using Light Localization and Channeling” awarded by the National Science Foundation.

FIELD OF THE INVENTION

This invention relates generally to sub-wavelength grating structures for enhanced transmission of incident optical radiation and, more particularly, to enhanced transmission sub-wavelength grating structures with polarization tunability and enhanced transmission sub-wavelength grating structures having geometries adapted to support coupled mode resonances for enhanced transmission and, in some embodiments, for light circulating or weaving. This invention further relates to devices that include such grating structures.

BACKGROUND OF THE INVENTION

There has been much interest in the phenomenon of enhanced transmission in periodically patterned metal structures, both in two-dimensionally periodic hole-arrays and in one-dimensionally periodic transmission grating structures. Referring to FIG. 1, enhanced transmission is a known phenomenon that can occur in certain conditions when light is incident on a periodically patterned optically-thick grating structure 10 having metal contacts 12. A typical Poynting vector 20 of the electromagnetic field incident 16 on the grating structure 10 is shown in FIG. 1 for illustration.

Enhanced transmission occurs when incident light 16 is transmitted with a transmittance (T) greater than a ratio of the area (A_(groove)) of grooves 14 that separate the contacts 12 to the total area of the structure 10 on which incident light 16 impinges (A_(total)), as described by Equation 1 below:

T>A _(groove) /A _(total).  (1)

Hence, the incident light 16 is channeled around the metal contacts 12 and through the grooves 14 of the grating structure 10 to transmit radiation 18. Structures with grooves having an area of only a few percent of the total area of the film have been found to transmit close to 100% of the incident light at particular wavelengths, polarization states and angles of incidence.

Enhanced optical transmission is an extremely useful property that can be exploited for use in a variety of optical devices, if it can be accurately modeled for different applications. Until fairly recently, this phenomenon was attributed to horizontally oriented surface plasmons (HSPs), surface plasmons that are oriented parallel to the surface, for both one-dimensional periodic grating structures and two dimensionally periodic hole arrays. Accordingly, these prior art enhanced transmission gratings have been limited to specific configurations designed to optimize HSP coupling.

For example, U.S. Pat. No. 5,973,316 to Ebbesen et al. (“Ebbesen”) discloses an array of low profile sub-wavelength apertures in a thin metallic film or thin metal plate for enhanced light transmission by coupling to an HSP mode, where the period of the array is chosen to enhance transmission within a particular wavelength range. Ebbesen further discloses that the array can be used to filter and collect light for photolithographic applications.

In another example, U.S. Pat. No. 5,625,729 to Brown discloses an optoelectronic device for resonantly coupling incident radiation to a local surface plasmon wave. The device, e.g., a metal-semiconductor-metal (“MSM”) detector, includes a multiplicity of substantially planar and regularly spaced low-profile electrodes on a semiconductor substrate to resonantly couple an HSP mode propagating along the grating and the substrate.

Those of ordinary skill in the art will appreciate that only incident transverse-magnetic (TM) radiation (defined as electromagnetic radiation with the magnetic field oriented parallel to the grating elements (wires, e.g.)) will couple to HSPs. Accordingly, these and other prior art sub-wavelength enhanced transmission gratings are limited to specific configurations designed to optimize HSP coupling and, consequently, to gratings which enhance transmission of TM radiation.

SUMMARY OF THE INVENTION

The present invention relates to polarization-tunable enhanced transmission sub-wavelength (PETS) gratings that can be tuned to selectively transmit a predetermined polarization state or to simultaneously enhance transmission of both TM and transverse-electric (TE) radiation. The present invention also relates to enhanced transmission sub-wavelength gratings that include structure that supports cavity modes (“CMs”), including hybrid cavity modes to produce light-circulating or light-weaving structures, depending on the angle of incident radiation. The gratings of the present invention advantageously have a small form factor, are easy to fabricate, and, consequently, are easy to integrate into devices requiring polarization-tunable transmission. Accordingly, the present invention further relates to devices that include any of the sub-wavelength gratings of the present invention.

A grating for enhancing transmission of incident electromagnetic radiation at a predetermined wavelength of the present invention includes a grating structure adapted to preferentially support cavity modes for coupling to and enhancing transmission of a transverse-electric (TE) polarization state of incident electromagnetic radiation. The grating structure includes a plurality of wires arranged with a periodicity that is equal to or less than the predetermined wavelength; and a groove between each adjacent pair of the plurality of wires. The groove includes a width between the wires and a height, wherein the groove is filled with a dielectric material having a dielectric constant equal to or greater than 1.

The grating can be a TE-polarizer with a transmission efficiency of at least 80%.

In one embodiment of any of the grating structures of the present invention, the dielectric constant is greater than or equal to 1.2. In another embodiment, the dielectric constant is greater than or equal to 2.0. In yet another embodiment, the dielectric constant is greater than or equal to 10, preferably greater than or equal to 14.

Any of the grating structures of the present invention can include an aspect ratio of the groove width to the periodicity in a range of at least 1 to less than or equal to 10.

Any of the gratings of the present invention can be adapted for enhancing transmission at a predetermined wavelength within a range of between; 1 nm and 400 nm; 400 nm and 700 nm; 0.7 microns and 100 microns; 100 microns and 1 mm; and 1 mm and 400 mm.

Any of the grating structures of the present invention can include wires that are formed from any highly conductive material, including one or more of aluminum, silver, gold, copper and tungsten.

Any of the grating structures of the present invention can be superposed on a substrate, which can include a plurality of layers, preferably where at least two layers are of different materials. Any of the substrates in the gratings of the present invention can include one or more of silica, silicon, silicon dioxide, Ge, GaAs, InP, InAs, AlAs, GaN, InN, GaInN, GaAlAs, InSb, fused silica, sapphire, quartz, glass, and BK7.

The dielectric material in the grooves of any of the grating structures of the present invention can include at least one of silica, silicon, silicon dioxide, silicon nitride, alumina, an elastomer, a crystalline powder, and a semiconductive material.

In other embodiments, the dielectric material can include one or more of crystalline ditantalum pentoxide, polycrystalline ditantalum pentoxide, crystalline hafnium oxide and polycrystalline hafnium oxide.

The present invention further includes a grating for enhancing transmission of incident electromagnetic radiation at a predetermined wavelength including a grating structure adapted to preferentially support cavity modes for simultaneously coupling to and enhancing transmission of a transverse-electric (TE) polarization state and a transverse-magnetic (TM) polarization state of incident electromagnetic radiation at the predetermined wavelength. The grating structure includes a plurality of wires arranged with a periodicity that is equal to or less than the predetermined wavelength; and a groove between each adjacent pair of the plurality of wires, the groove including a width between the wires and a height, and wherein the groove is filled with a dielectric material having a dielectric constant equal to or greater than 1.

One embodiment of the grating has a transmission efficiency of each of the TE and TM polarization state of at least 80%.

In one embodiment, the grating is adapted for use as an optical wavelength filter passing a band of the incident electromagnetic radiation including the predetermined wavelength, wherein the predetermined wavelength includes one of 650 nanometers, 750 nanometers, 850 nanometers, 1310 nanometers, 1330 nanometers, 1510 nanometers, and 1550 nanometers.

In another embodiment, the dielectric material includes at least one of silica, silicon, silicon dioxide, silicon nitride, alumina, an elastomer, a crystalline powder, a semiconductive material, crystalline ditantalum pentoxide, polycrystalline ditantalum pentoxide, crystalline hafnium oxide and polycrystalline hafnium oxide.

In other embodiments, the dielectric constant can be at least 2, at least 10, or at least 14.

The present invention further provides a grating including a grating structure adapted to preferentially support TE-excitable cavity modes at a first predetermined wavelength for coupling to and enhancing transmission of a transverse-electric (TE) polarization state of incident electromagnetic radiation at the first predetermined wavelength and to preferentially support TM-excitable cavity modes at a second predetermined wavelength for coupling to and enhancing transmission of a transverse-magnetic (TM) polarization state of incident electromagnetic radiation at the second predetermined wavelength. The grating structure includes: a plurality of wires arranged with a periodicity that is equal to or less than the predetermined wavelength; and a groove between each adjacent pair of the plurality of wires, the groove including a width between the wires and a height. The grating structure is further adapted to reflect the TM polarization state at the first predetermined wavelength and to reflect the TE polarization state at the second predetermined wavelength.

The present invention still further provides a grating for enhancing transmission of incident electromagnetic radiation at a predetermined wavelength that includes a grating structure adapted to preferentially support cavity modes for coupling to and simultaneously enhancing transmission of a TE-polarization state and a TM-polarization state at the predetermined wavelength. The grating structure includes a grating period that extends from a leading edge of a first wire in one of the sets to a leading edge of a first wire in the next set, so that a set of at least two wires and two grooves occurs within the grating period; i.e., the grating period includes two grooves per period. A first groove is between an adjacent pair of wires within each the set. Each first groove is associated with a first set of grating parameters including a first groove width, a first groove dielectric constant, and a first groove height. A second groove is between each repeating set of wires. The second groove is also associated with a second set of grating parameters including a second groove width, a second groove dielectric constant, and a second groove height.

In one embodiment, at least one of the first grating parameters differs from the corresponding second grating parameter by an amount that is sufficient to prevent the production of cavity modes in adjacent grooves that have overlapping transmission spectra.

In another embodiment, either the first width differs from the second width or the first dielectric constant differs from the second dielectric constant or both width and dielectric constant differ by a combined amount sufficient to prevent the production of cavity modes in adjacent grooves that have overlapping transmission spectra.

In yet another embodiment, the grating structure is further adapted.

A metal-semiconductor-metal detector device of the present invention includes a sensor for measuring an intensity of a transmitted TM and TE polarization state respectively at a predetermined wavelength and a grating for enhancing transmission of incident electromagnetic radiation at the predetermined wavelength that includes a grating structure adapted to preferentially support cavity modes for coupling to and simultaneously enhancing transmission of the TE-polarization state and the TM-polarization state at the predetermined wavelength and to preferentially transmit the TE-polarization state through the first grooves, and the TM-polarization state through the second grooves. The grating structure includes a grating period that extends from a leading edge of a first wire in one of the sets to a leading edge of a first wire in the next set, so that a set of at least two wires and two grooves occurs within the grating period; i.e., the grating period includes two grooves per period. A first groove is between an adjacent pair of wires within each the set. Each first groove is associated with a first set of grating parameters including a first groove width, a first groove dielectric constant, and a first groove height. A second groove is between each repeating set of wires. The second groove is also associated with a second set of grating parameters including a second groove width, a second groove dielectric constant, and a second groove height.

The present invention further includes a grating for enhancing transmission of incident electromagnetic radiation at a predetermined wavelength including a grating structure adapted to preferentially support cavity modes for coupling to and enhancing transmission of a predetermined polarization state at the predetermined wavelength, and for inducing light circulation or light weaving of the transmitted predetermined polarization state at the predetermined wavelength. The grating structure includes: a grating period having at least two grooves per grating period, a set of at least two wires occurring within each period, the grating period extending from a leading edge of a first wire in one of the sets to a leading edge of a first wire in the next one of the sets. The grating structure includes a first groove between an adjacent pair of wires within each set, where each first groove is associated with a first set of grating parameters including a first groove width, a first groove material having a first dielectric constant, and a first groove height. A second groove is between each adjacent set of wires, where the second groove is associated with a second set of grating parameters including a second groove width, a second groove material having a second dielectric constant, and a second groove height.

In one embodiment, one or more of the first grating parameters differs from the corresponding one or more of the second grating parameters by an amount that is sufficient to produce cavity modes in adjacent grooves that have overlapping transmission spectra.

In another embodiment, the first groove dielectric constant differs from the second groove dielectric constant and the first groove width differs from the second groove width.

A light storage device of the present invention includes an embodiment of the light circulating grating of the present invention.

The present invention further includes a grating for enhancing transmission of a predetermined polarization state of incident electromagnetic radiation at a predetermined wavelength that includes a grating structure adapted to support cavity modes that enhance transmission of the predetermined polarization state at the predetermined wavelength. The grating structure includes: a first layer of a first grating structure; a second layer of a second grating structure; and a dielectric layer between the first and second layers. The first grating structure includes a first period and is associated with a plurality of identical first grooves between a first pair of adjacent wires. One of the first grooves occurs within each of the first periods. The first groove includes a first groove height, a first groove width, and a first dielectric constant greater than or equal to 1. The second grating structure includes a second period and is associated with a plurality of identical second grooves between a second pair of adjacent wires. One of the second grooves occurs within each of the second periods. Each of the identical second grooves includes a second groove height, a second groove width, and a second dielectric constant greater than or equal to 1.

In one embodiment, the first grating structure is further associated with a plurality of identical third grooves between a third pair of adjacent wires. One of the first grooves and one of the third grooves is positioned within each of the first periods to form a multiple groove per period structure. The third groove has a third groove height, a third groove width, and a third groove dielectric constant equal to or greater than 1.

In yet another embodiment, the grating structure is further adapted to support cavity modes in adjacent grooves having overlapping transmission spectra, thereby producing light circulation or light weaving, depending on the angle of incident radiation.

In still another embodiment, the grating structure can be further adapted to localize the predetermined polarization state of incident electromagnetic radiation at the predetermined wavelength within the grating.

A grating of the present invention can include superposed layers of one or more of any of the grating structures of the present invention, preferably having a dielectric layer between each layer of grating structure. The dielectric layer(s) can include one or more of: one or more layers, each the one or more layers comprising at least one of crystalline silicon, poly-crystalline silicon, amorphous silicon, silicon oxide, silicon nitride, gallium arsenide, aluminum arsenide, gallium aluminum arsenide, indium phosphide, indium antimonide, indium phosphide antimonide, gallium nitride, indium nitride, gallium indium nitride, silica, borosilicate glass, mercury cadmium telluride, cadmium sulfide, cadmium telluride, a semiconductor material, an oxide, a polymer and plastic. Each of the dielectric layers can have a thickness of between 5 nm and 400 mm.

The present invention further provides a method of fabricating a waveband filter, the waveband filter including a grating structure adapted to enhance transmission of both transverse magnetic (TM) and transverse electric (TE) polarized incident electromagnetic radiation within a waveband that includes a predetermined wavelength, and a substrate on which the grating structure is superposed. The grating structure includes a groove dielectric constant ∈_(groove), a grating period Λ, a groove width, and a groove height. The method includes the following steps:

-   -   selecting the substrate with an index of refraction n_(s) and         the grating period Λ such that a first order diffraction occurs         at a wavelength λ equal to Λ/n_(s) that is less than the         predetermined wavelength;     -   selecting an initial value for the groove width, the groove         height and the groove dielectric constant that produce a         transmission curve for each of the TM and the TE polarized         radiation that at least partially falls within the waveband;     -   iteratively varying a value for the groove height from the         initial value and determining a wavelength of a transmission         intensity maximum of the TM-polarization state at the iterative         values for the groove height to determine an optimal groove         height for enhancing transmission of the TM-polarization state         at the predetermined wavelength;     -   for the optimal groove height and the initial value of the         groove dielectric constant, vary a value for the groove width         from the initial value until a transmission intensity maximum of         the TE-polarization state is aligned with the transmission         intensity maximum of the TM-polarization state at the         predetermined wavelength to obtain an optimal groove width; and     -   fabricating the grating structure having the initial value of         groove dielectric constant ∈_(groove), the optimal groove         height, and the optimal groove width on the substrate.         In one embodiment, the method further includes determining an         aspect ratio defined as groove height divided by groove width         and varying the aspect ratio, groove height and groove width to         adjust a width of the waveband and to align the TM- and         TE-polarization transmission curves to the predetermined         wavelength.

As a result, the present invention provides polarization-tunable enhanced transmission sub-wavelength (PETS) gratings that can be tuned to selectively transmit a predetermined polarization state or to simultaneously enhance transmission of both TM and transverse-electric (TE) radiation. In some embodiments, these PETS gratings are further adapted for light circulation or weaving. The present invention also provides enhanced transmission sub-wavelength gratings that include structure that supports cavity modes, including hybrid cavity modes, and devices that include any of the sub-wavelength gratings of the present invention. Such devices include polarizers, wavelength filters, light storage, memory, or controlling devices, and metal-semiconductor-metal photodetectors and polarization sensors.

Although illustrative embodiments of the present invention have been described herein with reference to the accompanying drawings, it is to be understood that the invention is not limited to those precise embodiments, and that various other changes and modifications may be effected therein by one skilled in the art without departing from the scope or spirit of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an illustration of enhanced transmission using a Poynting vector to represent light channeling through a cross-section of a single-groove-per-period grating.

FIG. 2 is a cross-sectional view of one embodiment of a single-groove-per-period grating structure of the present invention.

FIG. 3 is a top plan view of the embodiment of FIG. 2.

FIG. 4 is three-dimensional view of another embodiment of a single-groove-per-period grating of the present invention.

FIGS. 5A-5C are schematic representations of three different embodiments of a grating structure of the present invention for enhanced transmission of a predetermined polarization state at a predetermined wavelength.

FIG. 6 is a cross-sectional view of a representation of a grating structure of the present invention that can be adapted for any one of the embodiments of FIGS. 5A-5C.

FIG. 7 is a graphical representation of a dependence of peaks in transmission of different order modes for TE- and TM-polarization states on incident energy and groove width for an embodiment of a single groove per period grating structure of the present invention.

FIG. 8 is a transmission/reflectance plot for an embodiment of a grating structure of the present invention for simultaneous enhanced transmission of both TE and TM-polarized light at a predetermined wavelength.

FIG. 9 is a transmission/reflectance plot for an embodiment of a grating structure of the present invention for enhanced transmission of TE-polarized light at one predetermined wavelength and TM-polarized light at another predetermined wavelength.

FIGS. 10-12 are transmission/reflectance plots for particular embodiments of the grating structure of FIG. 5C for use as wavelength filters optimized at different predetermined wavelengths.

FIG. 13A is a cross-sectional view of an embodiment of a grating structure of the present invention having more than one groove per period.

FIG. 13B is a transmission plot of TE and TM-polarized states for a sub-grating structure of the grating structure of FIG. 13A.

FIG. 14 is a transmission plot of TE and TM-polarized states for another sub-grating structure of the grating structure of FIG. 13A.

FIG. 15 is a transmission plot of TE and TM-polarized states for an embodiment of the grating structure of FIG. 13A.

FIG. 16A is an SIBC modeled magnetic field density for a TM-polarized cavity mode (“CM”) in the embodiment corresponding to FIG. 15.

FIG. 16B is a Poynting vector representation of a TM-polarized CM in the embodiment corresponding to FIG. 15.

FIG. 17A is an SIBC modeled magnetic field density for a TE-polarized CM in the embodiment corresponding to FIG. 15.

FIG. 17B is a Poynting vector representation of a TE-polarized CM in the embodiment corresponding to FIG. 15.

FIG. 18 is a pictorial representation of a metal-semiconductor-metal device including an embodiment of the grating structure of the present invention.

FIGS. 19A and 19B are Poynting vector representations of an embodiment of a grating structure adapted to support light circulation in accordance with the present invention.

FIG. 20 is a Poynting vector representation of an embodiment of a grating structure adapted to support light weaving in accordance with the present invention.

FIG. 21 is a schematic representation of an embodiment of a device for light storage formed in accordance with the present invention.

FIG. 22 is a cross-sectional view of an embodiment of a layered grating structure formed in accordance with the present invention.

FIG. 23 is a flow chart representation of an embodiment of a method of the present invention.

FIG. 24 is a perspective view of a portion of an embodiment of a grating structure formed in accordance with the present invention providing a description of a coordinate system used to describe the grating structure.

FIG. 25 is a plot of the transmittance of the TM-polarized and TE-polarized CMs derived using an SIBC algorithm according to a method of the present invention for an embodiment of a grating structure of the present invention.

FIGS. 26 and 27 are plots of a full ω-k reflectance and transmittance profile of the TM-polarized and TE-polarized CMs, respectively, derived in accordance with a method of the present invention for the embodiment corresponding to FIG. 25.

FIGS. 28 and 29 are representations of the magnetic field and electric field intensities of the 25.188 GHz TM-polarized and TE-polarized CMs, respectively, derived in accordance with a method of the present invention for the embodiment corresponding to FIG. 25.

FIG. 30 is a representative plot of the experimental transmissivity data obtained for a sample of a grating structure formed in accordance with the present invention, which corresponds to the modeled grating structure described by FIGS. 25-29.

FIG. 31 is a cross-sectional view of an embodiment of a grating structure formed in accordance with the present invention.

FIG. 32 is a ω-k reflectance and transmittance profile for TE-polarized CMs for an embodiment of a grating structure of the present invention.

FIG. 33A is a ω-k reflectance and transmittance profile for TE-polarized CMs for another embodiment of a grating structure of the present invention that supports π resonances.

FIG. 33B is a Poynting vector representation of the embodiment corresponding to FIG. 33A.

FIGS. 34A and B are TE and TM Poynting vector representations of a light-circulating embodiment of a grating structure of the present invention.

FIG. 35 is a Poynting vector representation of a light-weaving embodiment of a grating structure formed in accordance with the present invention.

DETAILED DESCRIPTION

Referring to FIGS. 2-4, one embodiment of the sub-wavelength gratings formed in accordance with the present invention includes a polarization-tunable enhanced transmission sub-wavelength (PETS) grating 20 having a grating structure 22 that enhances transmission of a predetermined polarization state for a predetermined wavelength of incident radiation. The grating structure 22 includes a plurality of grooves 24 of refractive index n_(groove) (or dielectric constant ∈_(groove), where n_(groove)=√{square root over (∈_(groove))}) equal to or greater than 1 and having a width c 26, and a plurality of wires 28 defining a groove height 30 arranged with a center-to-center period Λ 32 that is less than the predetermined wavelength.

In one embodiment, as shown in FIGS. 2-4, the grating structure includes a single groove 24 per period Λ 32.

The grating structure 22, which is preferably superposed on a substrate 36, but may optionally be encased within a substrate material, is structured to support cavity modes (“CMs”) at a particular predetermined wavelength.

The grating structures of the present invention are optimized to support cavity modes at a particular predetermined wavelength, preferably within a particular band that includes the predetermined wavelength. One of ordinary skill in the art will recognize that the particular examples of grating structures provided herein can have dimensions scaled appropriately to a particular wavelength range of interest and include the corresponding appropriate materials for the wires and grooves and substrate material.

In particular, in various embodiments, any of the grating structures of the present invention can be adapted to support resonant modes at a predetermined wavelength between: 1 nm and 400 nm; 400 nm and 700 nm; 0.7 microns and 100 microns; 100 microns and 1 mm; and 1 mm and 400 mm.

The substrate in any of the gratings of the present invention can be composed of any dielectric suitable for the particular application, including any one or more of glass such as BK7, silica, fused silica, silicon dioxide (SiO_(2),)), silicon (Si), (including crystalline, poly-crystalline or amorphous), air, sapphire, quartz, or any or more semiconductor material, including III-IV and ternary compound semiconductors, including Ge (Germanium), Gallium Arsenide (GaAs), Indium Phosphide (InP), Indium Arsenide (InAs), Aluminum Arsenide (AlAs), Gallium Nitride (GaN), Indium Nitride (InN), Indium Antimonide (In Sb), Gallium Indium Arsenide (GaInAs), Gallium Indium Nitride (GaInN), Gallium Aluminum Arsenide (GaAlAs), and mercury cadmium telluride (HgCdTe).

The substrate can include more than one layer. Each of the multiple layers can be composed of a different material.

In one embodiment, the substrate includes an anti-reflective material.

Cavity modes (CMs), as referred to herein, are resonant modes produced within the grooves of a grating structure that satisfy the well-known Fabry-Perot resonance condition within the grooves. CMs include resonant modes produced by waveguide modes (WGs) of incident transverse-electric (TE) polarized radiation; and resonant modes produced by either WGs or vertically-oriented surface plasmons (VSPs) on the walls of the grooves of incident transverse-magnetic (TM) polarized radiation. The term “cavity mode”, in referring to the light circulating structures of the present invention also includes hybrid cavity modes that induce phase resonances.

TM-polarized (p-polarized) radiation is defined as electromagnetic radiation oriented so that its magnetic field is parallel to the grating wires. TE-polarized (s-polarized) radiation is electromagnetic radiation oriented so that its electric field is parallel to the grating wires.

The enhanced transmission gratings of the present invention are “sub-wavelength” gratings for enhancing transmission of incident electromagnetic radiation at a predetermined wavelength. “Sub-wavelength,” as referred to herein, means that a periodicity of the wires of the grating is equal to or less than the predetermined wavelength, so that the spacing between the wires is less than the predetermined wavelength.

The grating structures and gratings formed in accordance with the present invention, which enhance transmission of one or more polarization states to produce grating devices for various applications, are collectively referred to herein for convenience as “polarization-tunable enhanced transmission sub-wavelength” (“PETS”) grating structures and gratings. Use of this acronym is not to be construed in any way as limiting the grating structures of the present invention.

The wires of the present invention, which are also referred to as contacts, can be of any shape, size and of any material and arranged in any geometrical pattern to form a grating structure that preferentially supports CMs for enhancing transmission of a predetermined polarization state at a predetermined incident wavelength to form an embodiment of a grating structure of the present invention. For example, depending on the predetermined polarization state, predetermined wavelength, and desired application, the wires can be of a width that is 1%-95% relative to the period of the particular grating structure and of a height that is 1%-1000% relative to the period of a particular grating structure. The grooves in the grating structure preferably have widths of 1%4000% relative to the period.

The height “h” as referred to herein refers to a groove height, which is preferably equivalent to an adjacent wire height. However, it is contemplated to be within the scope of the invention to arrange the wires within recesses of a substrate, so that a wire height could be greater than an adjacent groove height. In such cases, the height h referred to herein is the groove height. It is also contemplated to provide different wires having different heights in a multiple-groove-per-period structure. In such cases, the height h referred to herein is a groove height corresponding to one of the adjacent wires.

Alternatively, the grating structures of the present invention can be formed from arrays of holes in thin (metallic) films.

Preferably, the wires in any of the grating structures can include any highly conducting metals, for example, any one or more of gold (Au), silver (Ag), aluminum (Al), copper (Cu), and tungsten.

In one embodiment, each wire has a quadrilateral cross-section such as rectangular, square, or trapezoidal. The intersection between the wires and the substrate is preferably formed of straight edges, but a curved or sloped interface can occur in the manufacturing process. This slight curvature of the interface does not affect the excitation of CMs, but it can shift the energy at which resonance occurs. Such shifts are preferably accounted for in the optimization of the grating structure parameters.

Referring to FIG. 4, in one embodiment, the grating structure 22 can include a material other than air superposed in a so-called “superstrate” layer 38 on top of the wires 28 and grooves 24. The layer 38 preferably includes a passivation or protective layer, and can be composed of materials such as a glass, oxide (e.g., SiO₂), polymer or plastic.

In a preferred embodiment, the grooves 24 are filled with a dielectric material having dielectric constant ∈_(groove) of at least 1.2, most preferably at least 2. In one embodiment, the dielectric constant ∈_(groove) of the material ranges from 2-20.

In another embodiment, the dielectric constant ∈_(groove) of the material in the grooves is at least 10, preferably at least 14. For example, the material in the grooves can be crystalline or polycrystalline ditantalum pentoxide or crystalline or polycrystalline hafnium oxide. These “high-K” materials, i.e., materials having a high dielectric constant, are particularly advantageous for TE-transmitting radiation, as described herein.

The grooves can be filled with air or with any material useful to the particular application. In one embodiment, the grooves 24 are filled with semiconductor materials, including one or more of silicon (Si), germanium, (Ge) and other III-V semiconductor compounds. The grooves can also be filled with at least one of silica, silicon, silicon dioxide, silicon nitride, alumina, an elastomer, and a crystalline powder.

Any of the grating structures or gratings of the present invention can also be adapted to localize a predetermined polarization state of incident electromagnetic radiation at a predetermined wavelength, and within a particular waveband, within the grating structure or grating.

The present invention is, in part, a result of the Applicants' efforts to accurately model the modes responsible for enhanced transmission in a known one-dimensional (1-D) sub-wavelength grating. Contrary to prior teachings on the subject that reported HSPs as primarily responsible for enhanced optical transmission (EOT), Applicants Crouse and Keshavareddy found and reported in a publication entitled “The role of optical and surface plasmon modes in enhanced transmission and applications, Optics Express, Vol. 13: Iss. 20, pp. 7760-7771 (Oct. 3, 2005) (“Crouse 2005”), the entirety of which is incorporated herein by reference thereto, that HSPs can both strongly inhibit and weakly enhance transmission in such sub-wavelength gratings. Applicants further reported that the predominant effect appeared to be a strong inhibition of transmission and interference with the transmission-enhancing properties of other resonant modes that could contribute to the phenomenon of enhanced transmission.

More recently, Applicants were able to theoretically show that cavity modes (CMs) in a lamellar grating structure can produce enhancements in transmission selectively for one or all polarizations of incident light. In addition, Applicants discovered that the properties of such CM-coupled grating structures (e.g., bandwidth, electromagnetic field profiles) and their dependencies on wavelength, angle of incidence, and structural geometries differ significantly from those of prior-art gratings optimized for HSP-induced enhanced transmission.

The formulation of the dependence of the parameters of a sub-wavelength grating on enhanced transmission was reported in Crouse and Keshavareddy, “Polarization independent enhanced optical transmission in one-dimensional gratings and device applications,” Optics Express, Vol. 15, No. 4, pp. 1415-127 (Feb. 19, 2007) (“Crouse 2007”), the entirety of which is incorporated herein in reference thereto.

In particular, Applicants have found that it is the cavity modes (CMs) defined herein, e.g., the resonant modes produced by WGs or the cavity mode component of a hybrid mode (consisting of both cavity resonance and surface plasmons resonance) that play the primary role in EOT of TE radiation, i.e., radiation polarized parallel to the metal wires.

Applicants have similarly found that similar cavity resonances can be found for TM radiation, i.e., for radiation polarized perpendicular to the wires, and that these resonances can help channel light through the grooves of the grating structure of the present invention to achieve enhanced optical transmission for this polarization state.

In other words, Applicants found that grating structures can be tailored to selectively support cavity modes corresponding to those modes that satisfy the Fabry-Perot condition inside the grooves, which can be preferentially excited by one or both of TM and TE-polarized radiation. Applicants further found that excitation of these cavity modes at a particular predetermined energy or wavelength can predictably provide enhanced transmission of one or both of TM and TE radiation through the grooves. It has also been found that the energy location of the peak transmission shifts to lower energies as the groove height or the dielectric constant of the groove is increased.

In optimizing the grating structure of the present invention to provide such polarization-tunable enhanced transmission, Applicants have surprisingly found that an essential design parameter in tuning the peaks of enhanced transmission for both TE and TM polarization states, not reported in the prior art, is the spacing between the wires, or the groove width c 26, referring to FIGS. 2-4, e.g. For a given polarization and fixed groove height and period, changes in the groove width alters the number of groove modes, energy at which EOT occurs, and the electromagnetic field distribution inside the grooves.

For TM-polarized light CMs produced in very narrow groove openings, the resonantly enhanced electromagnetic fields is relatively uniform throughout the groove and as the groove width is increased, the field redistributes with high intensity electromagnetic fields remaining close to the groove walls for wide openings. On the other hand, for TE polarization, the electromagnetic fields inside the grooves are concentrated more at the center of the groove, with very little fields on the side walls. As the groove width is increased, more resonance modes start occurring, redistributing the fields into lobes of high field intensities.

These characteristics and dependencies of CMs on the parameters of a grating structure are exploited, as described in more detail later in this specification, to form polarization-tunable enhanced transmission sub-wavelength (PETS) grating structures in accordance with the present invention by adapting and optimizing the grating structure parameters to selectively support the cavity modes that will couple to the predetermined polarization state (TE, TM or both, e.g.) at the predetermined wavelength.

Referring to FIG. 5A, one embodiment 40 of a PETS grating of the present invention includes a grating structure 42 that enhances transmission of TM-polarized radiation 44 at a predetermined wavelength and reflects TE-polarized radiation 46 to provide a “TE-pass” wavelength filter.

Referring still to FIG. 5B, another embodiment 48 of a PETS grating of the present invention includes a grating structure 50 that enhances transmission of TE-polarized radiation 52 at a predetermined wavelength and reflects TM-polarized radiation 54 to provide a “TM-pass” wavelength filter.

Yet another embodiment 56 of a PETS grating of the present invention shown schematically in FIG. 5C includes a grating structure 58 that simultaneously enhances transmission of TE 60 and TM-polarized radiation 62 at a predetermined wavelength.

Each grating structure of the PETS gratings shown in FIGS. 5A-5C includes wires of substantially rectangular cross-section formed in a one-dimensional (1D) grating structure that supports cavity modes, as described in further detail below in reference to FIG. 6. In the embodiments shown in FIGS. 5A-5C and 6, the grating structure includes a single groove per period.

The grating 70 of FIG. 6, includes a plurality of wires 72 arranged in a one groove 74 per period 76 structure 78 adapted to enhance transmission of a predetermined polarization state at a pre-determined wavelength. Each groove has a width c 80 and is filled with a material 88, which can be air or a material of index of refraction k, or dielectric constant ∈_(groove) (where ∈_(groove)=k²), greater than 1. Each wire 72 defines a groove height 82, has a width w 84, and is composed of gold. For the particular examples and plots described with reference to FIGS. 7-8, it is assumed that the grating structure 78 is free-standing; the “substrate” 36 is air.

In one embodiment of the grating 70, the periodicity A 76 is 1.75 microns, height h 82 is 1 micron, and silicon, a material having a dielectric constant ∈_(groove) of 11.9, fills the grooves 74. Using the methods of the present invention for modeling PETS gratings, one can generate a plot, as shown in FIG. 7, of the peak wavelength (energy) 90 of transmission for TM-polarized 92 and TE-polarized light 94 as a function of groove width 96 for the grating structure 78 having these parameters, with groove width varying from 0.35 microns to 0.66 microns. In FIG. 7, the 1st TM 91, 2nd TM 92, and 3rd TM 93 curves correspond to the three different orders of cavity mode resonance that occur when the grating is illuminated by light polarized parallel to the grid. Similarly, the 1st TE 97, 2nd TE 98, and 3rd TE 94 curves correspond to the three different orders of cavity mode resonance that occur when the grating is illuminated by light polarized perpendicular to the grid.

As can be seen from FIG. 7, the peak at which EOT occurs moves to higher energies for TM-polarized light and lower energies for TE-polarized light. It is also seen that for the particular parameters of the grating structure 78 chosen (Λ 76 of 1.75 microns, height h 82 of 1 micron, and groove ∈ of 11.9), an energy of 0.5 eV (2.5 μm) and a groove width 80 of 0.615 microns correspond to a point of intersection of the two curves 92 and 94. Therefore, an embodiment of a grating structure of the present invention that supports CMs for simultaneous EOT of TE and TM polarization at the same predetermined wavelength of 2.5 microns (μm), as described by FIG. 5C is achieved.

In one embodiment of the grating structure of the present invention, the dielectric material filling the grooves has a dielectric constant ∈_(groove) of at least 10, preferably at least 14. Applicants have determined that for grooves having a high dielectric constant, the grating structure of the present invention: provides TE-polarization enhanced transmission at lower energies than is possible without their use; inhibits TM-polarization transmission in gratings when there is not a TE-polarized CM excited; and allows alignment of TE-polarized and TM-polarized CMs at lower energies. Accordingly, a preferred embodiment of the grating structure that is tuned for simultaneous TE and TM transmission includes a dielectric constant ∈_(groove) of at least 10, preferably at least 14.

FIG. 8 shows a plot of the TM zero-order transmission 100 and TE zero-order transmission 102 curves as a function of energy for this embodiment. The TM reflectance 104 and TE reflectance 106 curves are also plotted for comparison.

Referring to FIG. 8, it can be concluded that for unpolarized incident light with an equal contribution from both polarization states (50% TM, 50% TE), as high as 94% of the incident light can be transmitted into a substrate 86 (FIG. 6). Accordingly, the methods of the present invention can be applied to effect significant design improvements in a variety of optoelectronic devices, particularly those requiring detection of polarization-independent radiation.

Starting again with an embodiment of the grating structure 78 shown in FIG. 6 having periodicity Λ 76 of 1.75 microns, height h 82 of 1 micron, and with silicon, ∈ of 11.9, filling the grooves 74, an embodiment of the grating structure 78 can be obtained by optimizing the groove width c 80 for enhancing transmission of either a TE- or TM-polarized radiation at a predetermined wavelength. In particular, by plotting the peaks of transmission for zero-order TM-polarized light and the dips of transmission for TE-polarized light as a function of groove width, the optimum groove width (point of intersection of the two curves) can be obtained to provide the PETS grating 40, in accordance with FIG. 5A, that enhances transmission of TM-polarized radiation 44 at a predetermined wavelength. Likewise, by plotting the peaks of transmission of TE-polarized light and dips of transmission of TM-polarized light, the optimum groove width can be determined to provide the PETS grating 48 in accordance with FIG. 5B, for enhancing transmission of TE-polarized radiation 44 at a predetermined wavelength.

In one particular embodiment, a groove width of 0.45 microns is chosen. FIG. 9 provides plots of the reflectance 110 and transmittance 112 of TE-polarized radiation, and of the reflectance 113 of and transmittance 114 of TM-polarized radiation as a function of incident energy of radiation. It can be seen from FIG. 9, that the grating structure 78 having these parameters (c of 0.45 microns, Λ 76 of 1.75 microns, height h 82 of 1 micron, and with silicon, E of 11.9, filling the grooves 74) is adapted to preferentially enhance transmission of TM-polarized light, as shown in FIG. 5A, for the predetermined wavelength of 3.729 microns (hw=0.333 eV). In another embodiment of the grating 70 having the same configuration and structural parameters, the structure 78 is adapted to enhance transmission of TE-polarized light, as shown in FIG. 5B, for the predetermined wavelength of 2.992 microns (hw=0.415 eV).

Accordingly, grating structure 78 having parameters c of 0.45 microns, A 76 of 1.75 microns, height h 82 of 1 micron, and ∈ of 11.9, also represents a grating structure that provides enhanced transmission of TM-polarized light at a first predetermined wavelength (0.45 microns in this example) and enhanced transmission of TE-polarized light at a second predetermined wavelength (3.729 microns in this example).

Referring to FIG. 9, even though the line-widths of the peak transmissions for TE 115 and TM-polarized radiation 116 for the structure are markedly different, it is possible to design narrow or broad peaks by changing a groove aspect ratio, defined herein as a groove height divided by groove width, depending on the application of interest. For example, photodetectors generally require a broad transmission peak, while wavelength filters may require narrow or broad transmission peaks depending on if they are being used as wavelength selectors or band-pass filters.

In a preferred embodiment, the aspect ratio is in a range of at least about 1 to less than about 10.

The PETS grating structures of the present invention can be used for many device applications including polarizers and wavelength filters. A preferred embodiment of a polarizer or wavelength filter formed in accordance with the present invention includes a PETS grating structure having only one groove per period, as described in reference to FIGS. 2-4, 5A-C and 6.

Examples of embodiments of narrow band filters formed from the PETS grating structures of the present invention optimized to simultaneously transmit both TE and TM incident radiation, as described in reference to FIG. 5C, are provided in FIGS. 10-12.

In particular, FIG. 10 provides a plot of normalized intensity 120 as a function of wavelength 122 for one embodiment of a narrow band optical wavelength filter formed in accordance with the present invention, optimized for enhanced transmission at of both TM and TE-polarized light at 850 nanometers (nm). The total transmission 124 and total reflection 126 curves for unpolarized incident radiation show that as high as 95% of un-polarized light can be transmitted into the substrate. In this embodiment of a 1-D periodic grating structure, in reference to FIG. 6, the wires 72 are composed of gold, the grating has a period 76 of 530 nm, the groove spacing 80 between the wires 72 is w=333 nm, and the height 82 defined by the metal contacts is h=490 nm. The grating structure 78 is positioned on top of substrate 86 of SiO₂, and the space between the wires is filled with dielectric material 88, SiO₂.

FIG. 11 provides a plot of normalized intensity 130 as a function of wavelength 132 for one embodiment of a narrow band optical wavelength filter formed in accordance with the present invention, optimized for enhanced transmission at of both TM and TE-polarized light at the telecommunication wavelength of 1330 nm. The total transmission 134 and total reflection 136 curves for unpolarized incident radiation show that as high as 82% of un-polarized light can be transmitted into the substrate. In this embodiment of a 1-D periodic grating structure, in reference to FIG. 6, the wires 72 are composed of gold, the grating has a period 76 of 850 nm, the groove spacing 80 between the wires 72 is w=260 nm, and the height 82 defined by the metal contacts is h=647 nm. The grating structure 78 is positioned on top of substrate 86 of SiO₂, and the space between the wires is filled with dielectric material 88, silicon.

FIG. 12 provides a plot of normalized intensity 133 as a function of wavelength 137 for one embodiment of a narrow band optical wavelength filter formed in accordance with the present invention, optimized for enhanced transmission at of both TM and TE-polarized light at the telecommunication wavelength of 1550 nm. The total transmission 135 and total reflection 138 curves for unpolarized incident radiation show that as high as 82% of un-polarized light can be transmitted into the substrate. In this embodiment of a 1-D periodic grating structure, in reference to FIG. 6, the wires 72 are composed of gold, the grating has a period 76 of 910 nm, the groove spacing 80 between the wires 72 is w=270 nm, and the height 82 defined by the metal contacts is h=575 nm. The grating structure 78 is positioned on top of substrate 86 of SiO₂, and the space between the wires is filled with dielectric material 88, silicon.

The PETS grating structures of the present invention adapted to support CMs produce within the grooves as described herein have a high degree of wavelength, bandwidth and polarization tunability and can, with the use of wires composed of low loss metals, and grooves and substrate materials composed of low-loss dielectrics, transmit close to 100% of the desired polarization component of the incident light.

In particular, in one embodiment of a PETS grating structure for enhanced transmission of either TE or TM polarization at a predetermined wavelength, at least 60% of incident TE or TM radiation respectively at the predetermined wavelength is transmitted.

In another embodiment of a PETS grating structure for enhanced transmission of either TE or TM polarization at a predetermined wavelength, at least 80% of incident TE or TM radiation respectively at the predetermined wavelength is transmitted.

In yet another embodiment of a PETS grating structure for enhanced transmission of either TE or TM polarization at a predetermined wavelength, at least 90% of incident TE or TM radiation respectively at the predetermined wavelength is transmitted.

In still another embodiment of a PETS grating structure for enhanced transmission of either TE or TM polarization at a predetermined wavelength, at least 95% of incident TE or TM radiation respectively at the predetermined wavelength is transmitted.

In one embodiment of a PETS grating structure for simultaneous enhanced transmission of TE and TM polarization at a predetermined wavelength, at least 60% of incident TE and TM radiation at the predetermined wavelength is transmitted.

In another embodiment of a PETS grating structure for simultaneous enhanced transmission of TE and TM polarization at a predetermined wavelength, at least 80% of incident TE and TM radiation at the predetermined wavelength is transmitted.

In yet another embodiment of a PETS grating structure for simultaneous enhanced transmission of TE and TM polarization at a predetermined wavelength, at least 90% of incident TE and TM radiation at the predetermined wavelength is transmitted.

In still another embodiment of a PETS grating structure for simultaneous enhanced transmission of TE and TM polarization at a predetermined wavelength, at least 95% of incident TE and TM radiation at the predetermined wavelength is transmitted.

The grating structures of the present invention described above in reference to FIGS. 1-12 and polarizer and wavelength filter devices incorporating these grating structures preferably include grating structures having one groove per period. Referring to FIG. 13A, another embodiment of a PETS grating structure 140 of the present invention includes more than one groove per grating period Λ 142. This type of structure 140 includes a pattern of repeating sets 144 of wires, where each wire in the set can have different characteristics; a first wire 145 in one set 144 is identical to the first wire 147 in the other sets, and so on. The grating period 142 has at least two grooves per grating period, where the grating period 142 extends, for example, from a leading edge 146 of one wire in one set 144 to a leading edge 148 of the corresponding wire in the adjacent set 150. Each set has at least a first groove 152 defined by a first width c₁ 154 and a first dielectric constant ∈_(1groove) between an adjacent pair of wires within each set 144 and a second groove 156 defined by a second dielectric constant ∈_(2groove) and a second width c₂ 158 between the last wire 160 in one set 144 and the adjacent first wire 162 in the next set 150 of wires.

The set 144 of wires can be composed of a pattern of wires of different materials, heights, and or shapes. In one embodiment, the grooves are composed of the same material. In other embodiments, the grooves are filled with different materials.

In one preferred embodiment, the grating structure 140 is adapted to preferentially support cavity modes for coupling to and simultaneously enhancing transmission of the TE-polarization state and the TM-polarization state at the same predetermined wavelength.

Preferably, the grating structure is further adapted to preferentially transmit the TM-polarization state through one set of grooves, for example, the first 152 narrower grooves, at the predetermined wavelength, and to preferentially transmit the TE-polarization state through the other set of grooves, for example, the second 156 wider grooves.

In one such embodiment, which is desirable for simple separation of polarized components of incident radiation, one or more of the groove parameters (e.g., groove width, dielectric constant) of the first groove differ(s) from that of the second groove by an amount sufficient to prevent the production of neighboring CMs that have overlapping shoulders within their transmission spectra. In one embodiment, only the groove widths differ, e.g., the first groove width 154 and second groove width 158 in FIG. 13A. Applicants surprisingly discovered that such overlap, rather than broadening the waveband of enhanced transmission as expected, creates hybrid coupled modes between the CMs produced in the first and second grooves that are undesirable for some applications. However, as discussed further below in regard to yet another embodiment, these hybrid CMs can advantageously be exploited to create a new so-called “circulating mode,” with unique device applications.

With reference to FIGS. 13-15, an embodiment of the grating structure 140 can be adapted to support CMs in two different grooves 152 and 156 within one period 142 of the grating structure 140 to preferentially transmit the TM-polarization state through one set of grooves, and the TE-polarization state through a second set of grooves. This embodiment can be described as a combination of two simple single-groove-per-period lamellar “sub-gratings,” having the same period 142 but different groove widths and/or dielectric contacts: (C₁, ∈_(1groove)) and (c₂, ∈_(2groove)). A specific example is provided in FIGS. 13-15. FIG. 13B shows the TM-polarization 166 and TE-polarization transmittance 168 for a first sub-grating 170 with Au wires 172, groove width 174 c=0.6 μm, height 176 h=0.645 μm, period 178 Λ=2.5 μm, dielectric constant 180 ∈_(groove)=22 (which is approximately the dielectric constant for Ta₂O₅) and air for the substrate and superstrate. Those parameters provide a TE-polarized CM at a predetermined λ=5 μm that selectively transmits TE-polarized light.

This TE-polarized mode corresponds to the n=m=1 mode found according to the formula for 100% confined (within the cavity) CMs provided by Equation (2) below:

$\begin{matrix} {\frac{2\pi}{\lambda_{peak}} = {n_{groove}\sqrt{\left( \frac{\pi \; n}{h} \right)^{2} + \left( \frac{\pi \; m}{c} \right)^{2}}}} & (2) \end{matrix}$

where n and m are integers and n_(groove)(=√{square root over (∈_(groove))}) is the index of refraction of the dielectric material in the grooves.

Referring to FIG. 14, if all the grooves are changed to have a width 184 of c=0.3 μm and dielectric constant 186 of ∈_(groove)=11.9 (≈∈_(silicon)) while everything else remains unchanged, to form a second “sub-grating” 182 shown in FIG. 14, this second single-groove-per-period grating has a TM-polarized CM 188 at λ=5 μm (the n=l, m=0 mode of Equation (2)) that selectively transmits TM-polarized light and the TE-polarization transmittance is zero for the wavelength range of 3-9 μm.

Referring to FIG. 15, if these two gratings 170 and 182 are combined to form the grating structure 190 with two grooves per grating, so that within one period 192 of 2.5 μm, there is one groove 194 with width 195 c=0.6 μm and ∈_(1groove)=22 and one groove 196 with 198 c=0.3 μm and ∈_(2groove)=11.9, the performance can be predicted. The transmittance of such a grating structure is approximately the normalized sum of the transmittance of the two constituent single-groove-per-period gratings shown in FIGS. 13B and 14, as long as there are no phase resonances produced, as discussed below. The TM-polarized light at λ=5 μm is transmitted through the narrower set of grooves, as described by field density 204 and Poynting vector plot 206 in FIGS. 16A and 16B respectively. The TE-polarized 202 light at λ=5 μm is transmitted through the wider set of grooves as described by the field density 208 and Poynting vector plot 210 in FIGS. 17A and 17B respectively. The normalized sum of the transmittances of the constituent single-groove-per-period gratings provides a good approximation of the transmittance of an embodiment of the multiple-groove-per period grating of the present invention for enhanced transmission and separation of both TM and TE polarization states, as long as the grating structure is adapted to preferentially support TM-polarized and TE-polarized CMs that are spaced far enough apart so that phase interactions do not occur.

Additional multiple-groove-per-period gratings for enhanced transmission and separation of predetermined polarization states are contemplated as being within the scope of the present invention. Such embodiments include a grating structure including a plurality of single-groove-per-period sub-grating structures, where each sub-grating structure is associated with grating parameters (including wire compositions, substrate material, periodicity, groove width, groove dielectric, period, wire height and shape, and so on), wherein at least one sub-grating structure differs sufficiently from another sub-grating structure to produce enhanced transmission without substantial phase interactions occurring between their associated CMs.

Referring to FIG. 18, in one embodiment of a device formed in accordance with the present invention, a metal-semiconductor-metal photodetector (MSM-PD) 212 that measures an incident beam's intensity and polarization state at a predetermined wavelength includes a multiple-groove-per period grating structure of the present invention. The MSM-PD 212 includes a grating structure 214 fabricated on top of an absorbing semiconductor substrate 216. The device 212 has alternately biased wires, positively biased 218 interspersed between negatively biased wires 220. This structure 214 has three grooves per period 222 with two of the grooves 224 being identical in every regard and selectively transmitting TM-polarized light and one of the grooves 226 selectively transmitting TE-polarized light. The transmitted light generates electron-hole pairs, producing electrical current components I_(p) and I_(s) due to the TM-polarization and TE-polarization components, respectively, of the incident beam. Readout integrated circuitry (ROIC) can then calculate I_(s) given I_(p) and I_(p)+I_(s). If desired, additional identical TE-polarized light channeling grooves can be inserted to allow for one set of contacts to only collect electron-hole pairs generated by TE-polarized light.

Referring to FIGS. 19A and 19B, another embodiment of the present invention includes a grating structure 230 having multiple-grooves-per-period 232 adapted to support hybrid CMs or “π” modes, which result from so-called phase resonances, that preferentially enhance transmission of a predetermined polarization states at a predetermined wavelength and also produce so-called “light circulation” 234 of the transmitted radiation through the structure 230 as illustrated by the Poynting vector representation in FIGS. 19A and 19B.

In this embodiment, the grating structure includes a plurality of grooves per period. Each groove within the period can be considered to be associated with a sub-grating structure that includes grating parameters (including wire compositions, substrate material, periodicity, groove width, groove dielectric, period, wire height and shape, and so on). At least one sub-grating structure differs sufficiently from another sub-grating structure to produce enhanced transmission and light-circulation, but not enough to prevent phase interactions occurring between their associated CMs.

Though TM-polarized π modes have been reported in the prior art, TE-polarized π modes and the light circulation effect have not. Referring to FIG. 19A, for example, light circulation, as referred to herein, occurs when incident light 234 is transmitted through one set of grooves 236 and then re-transmitted through a second set of preferably differently shaped or composed grooves 238, resulting in a high net reflectivity for the light at a predetermined wavelength, polarization and angle of incidence. Optionally, the same effect can be achieved using an array of holes in a thin (metallic) film.

The light circulating grating structures of the present invention include those that enhance transmission of and produce light-circulation of one or both of TM- and TE-polarized incident light. FIG. 19A shows a Poynting vector representation 248 of the circulating radiation for TE-polarized radiation at a wavelength just below that at which a transmission minimum occurs for the hybrid CMs, and FIG. 19B shows a Poynting vector representation 250 of the circulating radiation for TE-polarized radiation at a wavelength just less than that at which the transmission minimum occurs, causing a shift in the direction of circulation. Further details of these light-circulating modes are provided in Example 3 of the Examples section below.

In Example 3, one embodiment 230 of the grating structure adapted for enhanced transmission and light circulation of TE-polarized light formed in accordance with the present invention has two grooves per period 232, with a first groove width 240 c₁=0.755 microns and a second groove width 242 c₂=0.735 microns, and ∈_(1groove) equaling ∈_(2groove)=23. The wires are gold. This structure is a light-circulating structure for the TE-mode at a normal angle of incidence of the incident light.

In another embodiment of the grating structure described in Example 3 with reference to FIG. X8, if the groove dielectric are also changed so that ∈_(1groove) does not equal ∈_(2groove), but rather ∈_(1groove)=25 and ∈_(2groove)=21, then enhanced transmission and light circulation of TM-polarized light occurs for light at a normal angle of incidence. Accordingly, the light-circulating grating structures of the present invention can be adapted to produce hybrid CM or π modes for light-circulation of any predetermined polarization state at a predetermined wavelength.

Referring to FIG. 20, any of the light circulating grating structures can be a light weaving structure 260 at non-normal angles of incidence.

“Light weaving” occurs when incident electromagnetic radiation 262 with a nonzero in-plane momentum (i.e., momentum in the direction parallel to the surface of the wire) is woven through alternating grooves 264, localizing light near the wires as it travels parallel to them. The light weaving grating structures of the present invention can be useful for photodetectors or for the propagation of signals or data.

Referring to FIG. 21, in one embodiment, a device including a light-circulating grating structure 266 of the present invention is adapted for use with an incident pulsed light signal 270 that is short in time duration, i.e., a transient pulse, including ultrafast pulses and pulses with time durations on the order of less than a femtosecond to a microsecond, so that the light circulation modes 268 cause light to be continually circulated around the wires in the grating through grooves, which are optionally holes in a preferably metal film. Light circulation will continue even after the excitation beam 270 is extinguished. The circulating light can then be released from the grating structure 266 by a probe beam 272 from either the top or the bottom resulting in the controllable “stopping” and “releasing” of an emitted signal beam 274 that will radiate away from the structure 266 with a portion of the probe beam that is reflected. The grating structure 266 can be adapted for use in a light storage, or memory, or controlling device structure.

In yet another embodiment of the grating structure shown in FIG. 22 of the present invention, any combination of layers 282, 284, 286, for example, of any of the grating structures of the present invention, with or without substrates, can be combined and separated by spacer layers 288 and 290, e.g., to produce the desired light circulating modes.

Hole arrays in thin, preferably metal, films that are adapted and arranged to produce the light circulating modes described herein are also considered within the scope of this invention.

Methods

One embodiment of a method for tailoring any of the PETS grating structures of the present invention includes applying a coupled mode algorithm that uses the well-known surface impedance boundary conditions (SIBC) as described in Example 1 provided below in the “Examples” section.

Example 1 assumes normal incident radiation, but the grating structures of the present invention also include those optimized for enhanced transmission at any predetermined angle of incidence, depending on the particular application and desired result.

Various parameters, including wire compositions, refractive index of a groove material, substrate material, periodicity, groove width and height can be varied, as described in Example 1, to optimize parameters for the grating structure having enhanced transmission of the desired polarization state(s) at the desired predetermined wavelength and for a predetermined bandwidth.

The present invention, therefore, includes a method of optimizing the spacing between the wires, pitch, and orientation to exploit the optical and surface plasmon resonances effect, to achieve polarization independent enhanced optical transmission. These parameters can be optimized in accordance with the preferred wavelength, polarization, and angle of incidence in accordance with the present invention. The height defined by the metal wires can be further optimized to achieve different line widths for the transmission peaks.

In particular, one embodiment of the method of the present invention assumes, as an approximation, that the CMs are perfectly confined to the grooves. For CMs perfectly confined to the grooves, their wavelengths are given by Equation (3):

$\begin{matrix} {\frac{2\pi}{\lambda_{peak}} = {n_{groove}\sqrt{\left( \frac{\pi \; n}{h} \right)^{2} + \left( \frac{\pi \; m}{c} \right)^{2}}}} & (3) \end{matrix}$

where n and m are integers and n_(groove) (=√{square root over (∈_(groove))})_(is) the index of refraction of the dielectric material 88 in the grooves 74.

Even though CMs are not perfectly confined to the grooves, Equation (3) is still approximately true for CMs produced by waveguide modes and even for CMs produced by TM-polarized VSPs. More importantly, inherent in Equation (3) are the dependencies of the CMs on the structural parameters n_(groove), h, and c of the grating structures of the present invention, with the lowest m value allowable for TM-polarization (also referred to as “p-polarization”) and TE-polarization (also referred to as “s-polarization”) being m=0 and m=1 respectively. Because of this last fact, the lowest order TE-polarized CM occurs at a higher energy than the lowest energy p-polarized CM. Depending on the ratio of h/c, there can be many TM-polarized CMs with lower energies than the lowest energy TE-polarized CM, resulting in an undesirably large wavelength separation between the lowest order CMs for the different polarizations.

A more thorough description of all the dependencies of the TE-polarized and TM-polarized CMs on structural parameters (e.g., groove width, height and groove dielectric constant) is given in Crouse 2007, and also in Example 1 in the Examples section below.

Summarizing these dependencies, the TM-polarized CMs have strong dependencies on h and ∈_(groove) and a weak dependence on c if the m=0 mode is used. Also, TM-polarized CMs can have a strong dependence on Λ, especially when Λ is such to produce a Wood-Rayleigh anomaly (WR) or a HSP at a wavelength close in value to that of the CM. The TE-polarized CMs have strong dependencies on h, c, and ∈_(groove) and a weak dependence on Λ. With these basic characteristics and structural dependencies of the CMs in mind, one embodiment of a method for tuning (with respect to wavelength) the lower order TE-polarized CMs and TM-polarized CMs is provided as follows.

The method and gratings of the present invention allow for the use of a high-index (or high-k) dielectric material in the grooves, which has the following advantages. To achieve the highest degree of transmission of an incident beam of radiation into the 0th order (“straight-through”) transmitted beam, the transmission enhancing CMs for both TM and TE polarizations should occur at a lower energy than the onset of 1^(st) order diffraction. For the grating structure of the present invention superposed on a substrate (e.g., glass, semiconductors, and so on) with a dielectric constant of n_(substrate)=_(substrate)), the onset of 1^(st) order diffraction occurs for a wavelength λ_(1st order)=Λ/n_(substrate). For substrates other than air, realistic aspect ratios (height/width of the grooves), and with h small enough to produce TM-polarized CM transmission peaks that do not crowd together (i.e., the bandwidth of the transmission peaks is at least twice the wavelength separation of adjacent peaks), a material within the grooves with a dielectric constant at least as large as the substrate's is typically desirable to lower the energy of the TE-polarized CMs below the onset of 1^(st) order diffraction. Also, high-index dielectrics (e.g., high-k dielectrics, such as hafnium oxide or ditantalum pentoxide) inhibit TM-polarization transmission through the relatively wide TE-polarization transmitting grooves (relative to the width of TM-polarization transmitting grooves) when a TM-polarized CM is not excited.

Accordingly, with reference to FIG. 23, one embodiment 300 of the method of the present invention for tuning and aligning the CM-produced enhanced transmission peaks for TE-polarized and TM-polarized light incident on grating structures with only one groove per period includes the following series of steps:

-   -   1. Choose 302 a grating period Λ so that the onset of 1^(st)         order diffraction is at a lower wavelength than the         predetermined wavelength at which enhanced transmission is         desired; the grating period Λ is also chosen to be less than the         predetermined wavelength.     -   2. Choose 304 an initial value for c, h, and ∈_(groove) to get         the TE-polarized and TM-polarized CMs in the approximate         wavelength range desired, using the following relationships, as         discussed above. The larger h is, the closer spaced (in         wavelength) the CMs are for each polarization. The larger the         aspect ratio h/c is, the higher the Q-factor the CMs. Too large         of an aspect ratio, however, will produce large absorption for         real metals. Importantly, grooves that are wide enough to         support a TE-polarized CM will generally allow TM-polarized         light to be transmitted in appreciable amounts even when a         TM-polarized CM is not excited. One way around this problem is         to use a high-index dielectric that does two things: (1)         increases the effective width and height of the groove by a         factor of √{square root over (∈_(groove))} and (2) increases the         impedance for TM-polarized light, thereby reducing the         TM-polarization transmission when a TM-polarized CM is not         excited.     -   3. Vary 306 the groove height h from its initial value to obtain         an optimal groove height h for supporting the TM-polarized CM at         the desired wavelength.     -   4. Vary 308 the groove width c from its initial value until the         TE-polarized CM is aligned with the TM-polarized CM to obtain an         optimal value of groove width c. The alignment may be performed,         e.g., by plotting the peak TE and peak TM as a function of         wavelength and groove width, e.g., as shown in FIG. 7.

An example of a grating structure formed according to this method is provided as Example 2 in the Examples section below.

The optimized parameters determined in accordance with any of the methods of the present invention can be used to fabricate any of the grating structures of the present invention using any appropriate method of fabrication known to those of ordinary skill in the art for fabricating sub-wavelength gratings.

For example, for the grating structures optimized to enhance radiation at predetermined wavelengths in the ultraviolet, visible and near infrared, mid-infrared long wavelength infrared and very long wavelength infrared, standard microfabrication technologies can be used. Such fabrication methods can include physical deposition of the wires and groove and substrate materials such as metals, oxides and semiconductors by thermal evaporation, electron beam evaporation, sputtering, or chemical vapor deposition.

The grating structures of the present invention can be generated using photolithography or electron beam lithography along with wet chemical etching and/or reactive ion etching or ion beam milling. For structures that operate in wavelength regions longer than the very long wavelength infrared, such as the terahertz and microwave regions, less expensive fabrication techniques can be used, including computer numerical control (CNC) micro milling machines.

EXAMPLES Example 1

The optical and electromagnetic characteristics of lamellar gratings, such as those of the present invention, are modeled in this example using a coupled mode algorithm that uses the surface impedance boundary condition (SIBC) approximation. This method is described in detail in D. Crouse, “Numerical Modeling and Electromagnetic Resonant Modes in Complex Grating Structures and Optoelectronic Device Applications,” IEEE Trans. Electron Devices 52: 2365-2373 (2005), the entirety of which is incorporated herein by reference, and are only summarized here. Referring to FIG. 24, this method uses the following approximation relating the tangential components of the electric and magnetic fields at a dielectric/metal interface:

E _(∥) =Z{circumflex over (n)}×H _(∥)  (A1)

where Z=1/n_(metal), with n_(metal) being the complex index of refraction of the metal. This approximation is valid if the dielectric constant of the metal is much larger than the neighboring dielectric (which is largely true in the infrared and visible spectral regions).

FIG. 24 defines the coordinate system used in the calculation. Only one period of the grating is shown. In the calculations, the top layer is assumed to be air.

The electromagnetic fields are expressed as a linear combination of orthogonal modes as follows:

$\begin{matrix} {{f_{air}\left( {x,y} \right)} = {{\exp \left( {\left( {{\alpha_{0}x} - {\beta_{0}\left( {y - {h/2}} \right)}} \right)} \right)} + {\sum\limits_{n = {- \infty}}^{\infty}\; {R_{n}{\exp \left( {\left( {{\alpha_{n}x} + {\beta_{n}\left( {y - {h/2}} \right)}} \right)} \right)}}}}} & \left( {A\; 2} \right) \\ {\mspace{20mu} {{f_{groove}\left( {x,y} \right)} = {\sum\limits_{n = 0}^{\infty}{\Phi_{n}\left( {x,y} \right)}}}} & \left( {A\; 3} \right) \\ {\mspace{20mu} {{f_{substrate}\left( {x,y} \right)} = {\sum\limits_{n = {- \infty}}^{\infty}{T_{n}{\exp\left( {\left( {{\alpha_{n}x} - {{\overset{\sim}{\beta}}_{n}\left( {y + {h/2}} \right)}} \right)} \right.}}}}} & \left( {A\; 4} \right) \end{matrix}$

where f_(i)(x,y) is the {circumflex over (z)} component of the magnetic field or the {circumflex over (z)} component of the electric field depending on if the TM polarization or TE polarization is being modeled respectively. The other electric and magnetic field components can be obtained using relations derived from Maxwell's equations. Also, α_(n)=k_(o) sin θ_(incident)+nK, K=2π/d, β_(n)=√{square root over (k_(o) ²−α_(n) ²)}, {tilde over (β)}_(n)=√{square root over (∈_(substrate)k_(o) ²−α_(n) ²)} with n is an integer, d being the period of the structure θ_(incident) the angle of incidence, λ the wavelength, and ∈_(i) the dielectric constant of the i^(th) region. In Eqs. (A1) and (A3), the orthogonal modes used in the modal expansion are plane waves in the air and substrate layers and the following orthogonal modes Φ_(n)(x,y) are used in the grooves:

Φ_(n)(x,y)=X _(n)(x)Y _(n)(y)  (A5)

X _(n)(x)=d _(n) sin(μ_(n) x)+cos(μ_(n) x)  (A6)

Y _(n)(y)=a_(n)exp(iυ _(n) y)+b _(n)exp(−iυ_(n) y)(A7)

where the terms μ_(n) and υ_(n) obey the relation:

μ_(n) ²+υ_(n) ²=∈_(groove) k _(o) ²  (A8)

Applying the SIBC condition to the left-hand and right hand sides of the grooves results in the following equations (respectively):

$\begin{matrix} {d_{n} = \frac{\eta_{groove}}{\mu_{n}}} & \left( {A\; 9} \right) \\ {{\tan \left( {c\; \mu_{n}} \right)} = \frac{2\; \eta_{groove}\mu_{n}}{\mu_{n}^{2} - \eta_{2}^{2}}} & \left( {A\; 10} \right) \end{matrix}$

where c is the width of the groove and η_(groove)=k_(o)∈_(groove)Z/i for TM polarization and η_(groove)=k_(o)/iZ for TE polarization. The most essential step in the above method is the solution to Eqn. (A10). In this method the roots of Eqn. (A10) are found by integration starting from an initial value. We have performed the integration using the Runge-Kutta method.

Applying boundary conditions equating the tangential field components and the SIBC conditions at the metal/dielectric interfaces at y=h/2 and y=−h/2 yields the following equations.

$\begin{matrix} {\mspace{20mu} {{\sum\limits_{n = {- \infty}}^{\infty}{\left( {I_{n} + R_{n}} \right)^{{\alpha}_{n}x}}} = {{\sum\limits_{m}^{\infty}{{X_{m}(x)}\left( {{\phi_{m}a_{m}} + {\phi_{m}^{- 1}b_{m}}} \right)\mspace{14mu} 0}} \leq x \leq c}}} & \left( {A\; 11} \right) \\ {{{\sum\limits_{n = {- \infty}}^{\infty}{{\beta_{n}\left( {{- I_{n}} + R_{n}} \right)}^{{\alpha}_{n}x}}}} = \left\{ \begin{matrix} {\frac{\gamma_{air}}{\gamma_{groove}}{\sum\limits_{m}^{\infty}{{X(x)}{\upsilon_{m}\begin{pmatrix} {{\phi_{m}a_{m}} +} \\ {\phi_{m}^{- 1}b_{m}} \end{pmatrix}}}}} & {0 \leq x \leq c} \\ {\eta_{air}{\sum\limits_{n = {- \infty}}^{\infty}{\left( {I_{n} + R_{n}} \right)^{{\alpha}_{n}x}}}} & {c \leq x \leq d} \end{matrix} \right.} & \left( {A\; 12} \right) \\ {\mspace{20mu} {{\sum\limits_{n = {- \infty}}^{\infty}{T_{qn}^{{\alpha}_{n}x}}} = {{\sum\limits_{m}^{\infty}{{X(x)}\left( {{\phi_{m}^{- 1}a_{m}} + {\phi_{m}b_{m}}} \right)\mspace{14mu} 0}} \leq x \leq c}}} & \left( {A\; 13} \right) \\ {{{\sum\limits_{n = {- \infty}}^{\infty}{{\overset{\sim}{\beta}}_{n}T_{n}^{{\alpha}_{n}x}}}} = \left\{ \begin{matrix} {{- }\frac{\gamma_{substrate}}{\gamma_{groove}}{\sum\limits_{m}^{\infty}{{X_{m}(x)}{\upsilon_{m}\begin{pmatrix} {{\phi_{m}^{- 1}a_{m}} -} \\ {\phi_{m}b_{m}} \end{pmatrix}}}}} & {0 \leq x \leq c} \\ {\eta_{substrate}{\sum\limits_{n = {- \infty}}^{\infty}{T_{n}^{{\alpha}_{n}x}}}} & {c \leq x \leq d} \end{matrix} \right.} & \left( {A\; 14} \right) \end{matrix}$

where γ_(air)=∈_(air)=1, γ_(groove)=∈_(groove), γ_(substrate)=∈_(substrate), η_(air)=k_(o)Z/i and η_(substrate)=k_(o)∈_(substrate)Z/i for the TM polarization and γ_(air)=γ_(groove)=γ_(substrate)=1, η_(air)=η_(substrate)=k_(o)/iZ for the TE polarization and φ_(m)=e^(iυ) ^(m) ^(h/2).

Then multiplying Eqs. (A11) and (A13) by X_(m)(x) and integrating over the region 0≦x≦c and multiplying Eqs. (A12) and (A14) by e^(iα) ^(q) ^(x)/d and integrating over the region 0≦x≦d yields the following matrix equations that are used to determine the unknown coefficients R_(n), T_(n), a_(n) and b_(n):

$\begin{matrix} {\mspace{20mu} {{M\; \Psi} = \Omega}} & \left( {A\; 15} \right) \\ {\mspace{20mu} {with}} & \; \\ {M = \begin{pmatrix} G & {{- N}\; \phi} & {{- N}\; \phi^{- 1}} & 0 \\ {{\beta} - {\eta_{air}J}} & {{- }\frac{\gamma_{air}}{\gamma_{groove}}K\; {\upsilon\phi}} & {\frac{\gamma_{air}}{\gamma_{groove}}K\; {\upsilon\phi}^{- 1}} & 0 \\ 0 & {{- N}\; \phi^{- 1}} & {{- N}\; \phi} & G \\ 0 & {{- }\frac{\gamma_{substrate}}{\gamma_{groove}}K\; {\upsilon\phi}^{- 1}} & {\frac{\gamma_{substrate}}{\gamma_{groove}}K\; {\upsilon\phi}} & \begin{matrix} {{{- }\overset{\sim}{\beta}} +} \\ {\eta_{substrate}J} \end{matrix} \end{pmatrix}} & \left( {A\; 16} \right) \\ {\mspace{20mu} {\Psi = {{\begin{pmatrix} R \\ a \\ b \\ T \end{pmatrix}\mspace{14mu} {and}\mspace{14mu} \Omega} = \begin{pmatrix} {- {GI}} \\ {\left( {{\beta} + {\eta_{air}J}} \right)I} \\ 0 \\ 0 \end{pmatrix}}}} & \left( {{A17}\text{-}A\; 18} \right) \end{matrix}$

where the matrices φ, β, υ are square matrices with nonzero components along the main diagonal given by φ_(m), β_(n), υ_(m) that have been previously defined; G, N, J, K are matrices with components given by:

$\begin{matrix} {G_{mn} = {\int_{0}^{c}{{X_{m}(x)}{\exp \left( {{\alpha}_{n}x} \right)}{x}}}} & \left( {A\; 19} \right) \\ {K_{nm} = {\frac{1}{d}{\int_{0}^{c}{{X_{m}(x)}{\exp \left( {{- {\alpha}_{n}}x} \right)}{x}}}}} & \left( {A\; 20} \right) \\ {J_{qn} = {\frac{1}{d}{\int_{c}^{d}{{\exp \left( {{\left( {\alpha_{n} - \alpha_{q}} \right)}x} \right)}{x}}}}} & \left( {A\; 21} \right) \\ \begin{matrix} {N_{mn} = {\int_{0}^{c}{{X_{m}(x)}{X_{n}(x)}\ {x}}}} \\ {= {\delta_{mn}\left\lbrack {{\left( {\left( \frac{\eta_{groove}}{\mu_{m}} \right)^{2} + 1} \right)\frac{c}{2}} + \frac{\eta_{groove}}{\mu_{m}^{2}}} \right\rbrack}} \end{matrix} & \left( {A\; 22} \right) \end{matrix}$

The number of modes used in the electromagnetic field expansions were large and the solutions were convergent. The results obtained using the above approach were checked using another method that assumes that the walls of the grooves are perfectly conducting. These results yield practically identical results indicating that even though the convergence of TE polarization solutions using the SIBC approximation is worse than the convergence of TM polarization solutions, the main results showing EOT for both TM and TE polarizations will hold true when more accurate methods are used for the calculations.

Once Eq. (A15) is used to find all of the unknown coefficients, the reflectance (i=air in Eq. A23), transmittance and diffraction efficiencies (i=substrate in Eq. A23) can be calculated as the ratio of the {circumflex over (γ)}-component of the Poynting vector for an outward propagating mode and the {circumflex over (γ)}-component of the incident beam (assuming a normalized incident beam and a top layer being air):

$\begin{matrix} {{\frac{S_{y,n}}{S_{y,{incident}}}} = {\frac{\sqrt{ɛ_{i}}}{\gamma_{i}}\frac{\cos \; \theta_{{outward},n}}{\cos \; \theta_{incident}}{\Psi_{{outward},n}}^{2}}} & \left( {A\; 23} \right) \end{matrix}$

where Ψ_(outward,n) is either R_(n) or T_(n) and θ_(output,n) is the angle of the outward propagating mode.

Example 2

Referring to FIG. 5C and FIG. 6, an embodiment of the single-groove-per-period grating structure 58 was fabricated for enhanced transmission of both TE-polarized and TM-polarized microwaves at a predetermined frequency of 25.188 GHz (wavelength λ=11.91 mm). The grating structure has Al contacts or wires (∈_(Al)/=−10⁴+i·10 ⁷), a period of 10.3428 mm, groove width of 3.8211 mm, thickness of 6.045 mm, groove dielectric constant of 2.8, and air for the substrate and superstrate. The experimental results for this simple grating structure verified the accuracy of the numerical modeling algorithms provided herein and the concepts of CM-induced enhanced transmission, thereby allowing for these algorithms and concepts to also be used in the design of more complex grating structures having more than one groove per period, as shown, for example, in FIG. 22.

Two numerical modeling methods were used and their results compared to ensure agreement and accuracy. One method uses the surface impedance boundary condition (SIBC) approximation and allows for very quick calculation of all optical characteristics of a wide range of grating structures. The other method is the finite-element method solver HFSS™ commercially available from Ansoft Corp. Note that CMs, HSPs, VSPs, WRs, diffraction and all other optical effects occur in the microwave as they do in the infrared (IR) and visible spectral regions but the CMs and diffraction features occur at wavelengths that scale with groove height and width and grating pitch or period. The transmittance (FIG. 25), the full ω-k reflectance and transmittance profiles (FIGS. 26-29), and the magnetic field and electric field intensities of the 25.188 GHz TM-polarized and TE-polarized CMs respectively were obtained using the SIBC algorithm. The normal incidence transmittance and reflectance were also obtained using HFSS™ (results of which are not shown for the sake of clarity and brevity) and agreed with the SIBC results. Properties of the TM-polarized and TE-polarized CMs are also discussed in Crouse 2005 and Crouse 2007 and can be seen in these FIGS. 26-29, including the high transmittance, the small angle of incidence dependence, and the interaction and anti-crossing of TM-polarized CMs and WRs.

The fabricated device was formed in accordance with the methods presented herein to produce cavity modes that simultaneously couple to TM- and TE-polarized radiation at the predetermined wavelength of 11.91 mm. Such millimeter-scale structures are far cheaper and quicker to fabricate than their nanoscale counterparts, and they can provide just-as-good experimental verification of the pertinent theoretical constructs, since the effects and wavelengths of the WRs and CM modes responsible for the device performance all scale with the device dimensions. In the case of periodic features on a millimeter scale, for example, theory predicts that enhanced transmission will be observed in the microwave spectral region. In moving from the IR to microwave spectral region, the only difference between the reflectivity and transmittance curves is the slightly higher energies and intensities for the HSP and CM resonances, as metals in the microwave behave as almost perfect conductors; the dielectric constant of Al that is used is ∈_(Al)=−10⁴+i·10 ⁷ for the microwave to λ=31 μm and tabulated data²⁶ from λ=31 μm to λ=600 nm. Additionally, unlike studies undertaken in the visible or even the IR, we need not worry about variation in the permittivity of the materials used; essentially the metal is perfectly conducting, and the dielectric filling the grooves is virtually non-dispersive at these wavelengths. It is therefore a very sensible approach to undertake these proof-of-principle studies at longer wavelengths.

The experimental sample was constructed by machining a set of identical grooves, each of width c=3.82 mm, spaced with a periodicity of 10.34 mm and milled all the way through an aluminum alloy plate of thickness h=6.05 mm to cover an area of approximately 400 mm×400 mm. The voids were then carefully filled with an elastomer (Dow Corning® Sylgard® 184 silicone encapsulant) that had been mixed and left to rest under vacuum until completely evacuated. The real part of the permittivity of the elastomer is ˜2.8 in the GHz regime. Linearly polarized microwave radiation from a standard gain horn was collimated using a spherical mirror to impinge upon the sample at normal incidence. A continuous wave source sweeps the frequency in bands 18≦ν≦26.5 GHz and 26.5≦ν≦40 GHz (i.e., 7.5≦λ≦16.7 mm) and feeds the fixed position antenna. Before striking the sample, the incident beam was passed through an aperture of a broadband microwave absorbing material in order to restrict the incident beam spot to the useful sample area. Furthermore, in order to obtain averaging of the transmitted signal over a large number of grating periods, the transmitted beam is collected using another spherical mirror before being focused into a second horn antenna and detector. The polarization of both the incident beam and that detected can be altered in this configuration via simple rotation of each horn antennae about its central axis.

The experimental transmissivity data, setting both the incident and detected polarizations to either TM-polarization 400 or TE-polarization 402, normalized to a spectrum in the absence of the sample, are shown in FIGS. 30 (+ and ◯ respectively). As is seen in FIG. 30, the experimental transmittivities are substantially reduced relative to the predicted values 404 and 406 respectively obtained by numerical modeling, however once a small absorptive component, associated with a Debye dielectric response of the polymer and impurities, is included in the dielectric constant of the elastomer used in the modeling, the modeled 408 and 410 respectively and experimental curves 400 and 402 match very well. Hence, by fitting the experimental data to the modeling, it was found that the structure that was fabricated had a groove width of 3.824 mm and a dielectric constant for the groove of ∈_(groove)=2.75+i·0.0945. The magnitude of these dielectric losses can be reduced by the use of crystalline powders instead.

Example 3

It is known that phase resonances for TM-polarized incident light can arise in gratings that have multiple grooves per period that differ with respect to composition, geometry or orientation. In these types of structures, TM-polarized VSP-CMs in neighboring grooves can couple, producing field profiles of equal magnitude but with a π radians phase difference; such modes have come to be called π modes or resonances, as described, for example, in Alastair P. Hibbins, et al., Physics Review Letters 96 257402 (2006). However, light-circulation has not been previously reported for any polarization.

For TE-polarized light, there is no component of the electric field that is normal to any metal/dielectric interface, and hence SPs and VSP-CMs cannot be excited. However, Applicants have found that WG-CMs do occur, and along with Rayleigh anomalies, are responsible for a large number of the enhanced or anomalous optical effects, including TE-polarized π modes with properties similar to the properties of TM-polarized π modes. The light circulation and weaving effects of the multiple-groove-per-grating structures formed in accordance with the present invention have been found by Applicants to occur for both s-polarized and p-polarized incident light.

To demonstrate a grating structure adapted to support hybrid CMs for inducing light circulation in accordance with the present invention, two grating structures are discussed in reference to FIG. 31. These two grating structures exhibit many anomalous optical characteristics for both TM-polarized (also referred to herein as p-polarized) and TE-polarized (also referred to herein as s-polarized) incident light. The first grating, denoted as Grating 1, has identical grooves with widths c=0.745 μm, height h=1 μm, dielectric ∈=23, period Λ=1.75 μm, gold for the wires and air as the superstrate and substrate. As is shown in FIG. 32, this structure exhibits a number of WG-CM bands that produce s-polarization enhanced transmission (this structure also exhibits p-polarization enhanced transmission (not shown)).

If the widths of the grooves are perturbed so that every other groove has a width of c₁=0.755 μn and the rest of the grooves have widths of c₂=0.735 μm while keeping all the other parameters unchanged, the resulting structure is the two-groove-per period Grating 2 of FIG. 31. The band folding techniques described, e.g., in Crouse 2005 can be used to construct the approximate shapes of the resulting photonic and plasmonic bands. For s-polarization, such band folding is not necessary because the WG-CM bands are satisfactorily explained by the fact that the two WG-CMs in the two dissimilar, neighboring grooves have slightly different resonant frequencies, causing each of the original bands in the single-groove-per-period grating to split into two bands that interact with each other.

FIG. 33A shows the full ω-k diagram showing that the s-polarized WG-CMs are more complex than the WG-CMs shown in FIG. 32 for the single-groove-per-grating structure, with every CM band split into two CM bands that are separated by an s-polarized π mode producing a transmission minimum at an energy of 0.24815 eV. Also, additional diffraction modes and CM/diffraction interactions are produced.

Many similarities and several important differences between s-polarized and p-polarized π modes exist. The Poynting vector representation of FIG. 33B shows an s-polarized it mode with a π radian difference in the phase of H in neighboring grooves that is similar to the π radian difference in the phase of E in neighboring grooves for p-polarized π modes. However, the dispersions of all the s-polarization bands are far less than the dispersion of p-polarized photonic bands. Another important difference is that s-polarized π modes are necessarily produced by coupled WG-CMs because of the absence of SPs.

The incident beam cannot directly couple to the π radian out-of-phase field in every other groove. Because of this fact, the π resonances will always be located on the shoulders of the broad transmission peak. Applicants have observed in numerous two-groove-per-period gratings that the s-polarized π modes tend to be closer to the center of the transmission peak than the p-polarized π modes. This property arises because of the different components that make up the s-polarized and p-polarized π modes. Applicants have found that the components of the s-polarized π mode are two very similar, inherently radiative, WG-CMs that have slightly different resonant frequencies. The alternating groove width perturbation simply splits the original WG-CM band into two bands that are slightly asymmetric bands because the π resonance still has to occur on the shoulder of the original WG-CM transmission peak, but typically more symmetric than the two transmission peaks one either side of a p-polarization π mode. This greater symmetry affects the light circulation produced by π mode.

By examining the power flow, Applicants found that at or around the transmission minimum produced by the π modes, light is transmitted with high transmissivity through the two sets of grooves but then circles around, and is transmitted with high transmissivity through the neighboring grooves, resulting in a reflection maximum. It is clear that π modes are hybrid modes, composed of two coupled s-polarized WG-CMs. Furthermore, at the transmission minimum, these two transmission channels, created by the two coupled CMs, are equal in magnitude but produce counter propagating circulations of light resulting in high field intensities in the grooves but a net zero power flow in the grooves as equal amounts of power flow up and down each groove.

FIGS. 34A and B show the Poynting vector profiles for s-polarized light at energies slightly smaller and larger than the wavelength of the transmission minimum respectively. One of two things occurs on either side of the π resonance transmission minimum, depending on whether it is a p-polarized or s-polarized π mode, however both things involve a competition between the two transmission channels produced by the two coupled CMs in neighboring grooves. Focusing on the s-polarization, on either side of the more symmetric s-polarized π resonance transmission minimum (more symmetric compared to p-polarized π modes), one transmission channel associated with one set of grooves becomes weaker than the other transmission channel associated with the other set of grooves. Thus, of the two transmission channels that are presented to incident light, larger amounts of power are transmitted through the stronger transmission channel (i.e., one set of grooves) relative to the weaker transmission channel (i.e., the other set of grooves).

However, the weaker transmission channel is still strong enough to present to the now transmitted light on the substrate side, a strong and viable transmission channel back through the grating. This weaker transmission channel is the only channel possible because the transmitted light will not curve 180° and go back through the same groove through which it was initially transmitted. The net result of this process is a high reflectance. For energies progressively further from the transmission minimum, the weaker transmission channel re-transmits progressively lesser amounts of light which had been transmitted to the substrate via the stronger transmission channel, resulting in decreasing light circulation and increasing transmissivity.

Referring to FIG. 35, for off-normal incident angle, this light circulation turns into light weaving for the particular grating parameters applied, as the light weaves its way back and forth through the structure while having a net power flow in one direction. Numerous other structures with more than two grooves per period are within the cope of this invention, including those with multiple layers of multiple-groove-per-period gratings, in which light weaves and circulates around the metal wires in increasingly complex ways.

Though specific examples of PETS gratings for enhanced TM, TE or simultaneous enhanced TM- and TE-transmission and also those optimized for light circulation and weaving are described herein, one of ordinary skill in the art will recognize that various known methods can be used to iteratively vary one or more parameters of the grating structure to optimize the design of any grating structure adapted to support CMs as described herein. As a result, it is understood that the scope of the present invention includes any sub-wavelength grating structure adapted to support CMs at a predetermined wavelength as described herein, including any grating structure formed in accordance with any embodiment of the method of the present invention for optimizing and tuning the grating structures, described herein including in the “Examples” section.

Although illustrative embodiments of the present invention have been described herein with reference to the accompanying drawings, it is to be understood that the invention is not limited to those precise embodiments, and that various other changes and modifications may be effected therein by one skilled in the art without departing from the scope or spirit of the invention. 

1. A grating for enhancing transmission of incident electromagnetic radiation at a predetermined wavelength comprising: a grating structure adapted to preferentially support cavity modes for coupling to and enhancing transmission of a transverse-electric (TE) polarization state of said incident electromagnetic radiation, said grating structure comprising: a plurality of wires arranged with a periodicity that is equal to or less than said predetermined wavelength; and a groove between each adjacent pair of said plurality of wires, said groove including a width between said wires and a height, wherein said groove is filled with a dielectric material having a dielectric constant equal to or greater than
 1. 2. The grating of claim 1, wherein said plurality of wires comprise at least one of aluminum, silver, gold, copper and tungsten.
 3. The grating of claim 1, further comprising a substrate on which said grating structure is superposed.
 4. The grating of claim 3, wherein said substrate comprises a plurality of layers, said plurality of layers comprising at least two layers of different material.
 5. The grating of claim 3, wherein one of said plurality of layers is an antireflective coating.
 6. The grating of claim 3, wherein said substrate comprises one of silica, silicon, silicon dioxide, Ge, GaAs, InP, InAs, AlAs, GaN, InN, GaInN, GaAlAs, InSb, fused silica, sapphire, quartz, glass, and BK7.
 7. The grating of claim 1, wherein said grating is a TE-polarizer with a transmission efficiency of at least 80%.
 8. The grating of claim 1, wherein said dielectric constant is greater than or equal to 1.2.
 9. The grating of claim 1, wherein said dielectric constant is greater than or equal to 2.0.
 10. The grating of claim 1, wherein said dielectric constant is greater than or equal to
 10. 11. The grating of claim 1, wherein said dielectric constant is greater than or equal to
 14. 12. The grating of claim 1, wherein said dielectric material comprises at least one of silica, silicon, silicon dioxide, silicon nitride, alumina, an elastomer, a crystalline powder, and a semiconductive material.
 13. The grating of claim 1, wherein said dielectric material comprises one or more of crystalline ditantalum pentoxide, polycrystalline ditantalum pentoxide, crystalline hafnium oxide and polycrystalline hafnium oxide.
 14. The grating of claim 1, said grating structure further comprising an aspect ratio of said groove width to said periodicity in a range of at least 1 to less than or equal to
 10. 15. The grating of claim 1, wherein said predetermined wavelength is in a range of between 1 nm and 400 nm.
 16. The grating of claim 1, wherein said predetermined wavelength is in a range of between 400 nm and 700 nm.
 17. The grating of claim 1, wherein said predetermined wavelength is in a range of between 0.7 microns and 100 microns.
 18. The grating of claim 1, wherein said predetermined wavelength is in a range of between 100 microns and 1 mm.
 19. The grating of claim 1, wherein said predetermined wavelength is in a range of between 1 mm and 400 mm.
 20. A grating for enhancing transmission of incident electromagnetic radiation at a predetermined wavelength comprising: a grating structure adapted to preferentially support cavity modes for simultaneously coupling to and enhancing transmission of a transverse-electric (TE) polarization state and a transverse-magnetic (TM) polarization state of said incident electromagnetic radiation at said predetermined wavelength, said grating structure comprising: a plurality of wires arranged with a periodicity that is equal to or less than said predetermined wavelength; and a groove between each adjacent pair of said plurality of wires, said groove including a width between said wires and a height, and wherein said groove is filled with a dielectric material having a dielectric constant equal to or greater than
 1. 21. The grating of claim 20, wherein a transmission efficiency of each of said TE and TM polarization state is at least 80%.
 22. The grating of claim 20, adapted for use as an optical wavelength filter passing a band of said incident electromagnetic radiation including said predetermined wavelength, wherein said predetermined wavelength includes one of 650 nanometers, 750 nanometers, 850 nanometers, 1310 nanometers, 1330 nanometers, 1510 nanometers, and 1550 nanometers.
 23. The grating of claim 20, wherein said dielectric material comprises at least one of silica, silicon, silicon dioxide, silicon nitride, alumina, an elastomer, a crystalline powder, a semiconductive material, crystalline ditantalum pentoxide, polycrystalline ditantalum pentoxide, crystalline hafnium oxide and polycrystalline hafnium oxide.
 24. The grating of claim 20, wherein said dielectric constant is at least
 14. 25. The grating of claim 20, wherein said dielectric constant is at least
 10. 26. The grating of claim 20, wherein said dielectric constant is at least
 2. 27. The grating of claim 20, said grating further comprising a substrate on which said plurality of wires is superposed wherein said substrate comprises one of silica, silicon, silicon dioxide, Ge, GaAs, InP, InAs, AlAs, GaN, InN, GaInN, GaAlAs, InSb, fused silica, sapphire, quartz, glass, and BK7.
 28. A grating comprising: a grating structure adapted to preferentially support TE-excitable cavity modes at a first predetermined wavelength for coupling to and enhancing transmission of a transverse-electric (TE) polarization state of incident electromagnetic radiation at said first predetermined wavelength and to preferentially support TM-excitable cavity modes at a second predetermined wavelength for coupling to and enhancing transmission of a transverse-magnetic (TM) polarization state of incident electromagnetic radiation at said second predetermined wavelength; said grating structure comprising: a plurality of wires arranged with a periodicity that is equal to or less than said predetermined wavelength; and a groove between each adjacent pair of said plurality of wires, said groove including a width between said wires and a height, and wherein said grating structure is further adapted to reflect said TM polarization state at said first predetermined wavelength and to reflect said TE polarization state at said second predetermined wavelength.
 29. The grating of claim 28, wherein said dielectric constant is at least
 2. 30. The grating of claim 28, wherein said dielectric constant is at least 1.2.
 31. A grating for enhancing transmission of incident electromagnetic radiation at a predetermined wavelength comprising: a grating structure adapted to preferentially support cavity modes for coupling to and simultaneously enhancing transmission of a TE-polarization state and a TM-polarization state at said predetermined wavelength, said grating structure comprising: a grating period comprising a set of at least two wires, said grating period comprising at least two grooves per grating period, said grating period extending from a leading edge of a first wire in one of said sets to a leading edge of a first wire in the next one of said sets; a first groove between an adjacent pair of wires within each said set, each said first groove associated with a first set of grating parameters including a first groove width, a first groove dielectric constant, and a first groove height; and a second groove between each said set of at least two wires, each said second groove associated with a second set of grating parameters including a second groove width, a second groove dielectric constant, and a second groove height.
 32. The grating of claim 31, wherein one or more of said first grating parameters differs from the corresponding one or more of said second grating parameters by an amount that is sufficient to prevent the production of cavity modes in adjacent grooves that have overlapping transmission spectra.
 33. The grating of claim 32, wherein at least one of said first width differs from said second width and said first dielectric constant differs from said second dielectric constant.
 34. The grating of claim 31, wherein said grating structure is further adapted to preferentially transmit said TE-polarization state through said first grooves, and to preferentially transmit said TM-polarization state through said second grooves.
 35. The grating of claim 31, said grating further comprising a substrate on which said grating structure is superposed wherein said substrate comprises one of silica, silicon, silicon dioxide, Ge, GaAs, InP, InAs, AlAs, GaN, InN, GaInN, GaAlAs, InSb, fused silica, sapphire, quartz, glass, and BK7.
 36. A metal-semiconductor-metal detector device comprising the grating of claim 34, said device further comprising a sensor for measuring an intensity of said transmitted TM and said TE polarization state respectively at said predetermined wavelength.
 37. A grating for enhancing transmission of incident electromagnetic radiation at a predetermined wavelength comprising: a grating structure adapted to preferentially support cavity modes for coupling to and enhancing transmission of a predetermined polarization state at said predetermined wavelength, and for inducing light circulation or weaving of said transmitted predetermined polarization state at said predetermined wavelength, said grating structure comprising: a grating period comprising a set of at least two wires, said grating period comprising at least two grooves per grating period, said grating period extending from a leading edge of a first wire in one of said sets to a leading edge of a first wire in the next one of said sets; a first groove between an adjacent pair of wires within each said set, each said first groove associated with a first set of grating parameters including a first groove width, a first groove material having a first dielectric constant, and a first groove height; and a second groove between each said set of at least two wires, each said second groove associated with a second set of grating parameters including a second groove width, a second groove material having a second dielectric constant, and a second groove height.
 38. The grating of claim 37, wherein one or more of said first grating parameters differs from the corresponding one or more of said second grating parameters by an amount that is sufficient to produce cavity modes in adjacent grooves that have overlapping transmission spectra.
 39. The grating of claim 37, wherein said first groove dielectric constant differs from said second groove dielectric constant and said first groove width differs from said second groove width.
 40. The grating of claim 38, said grating further comprising a substrate on which said plurality of wires is superposed, wherein said substrate comprises one of silica, silicon, silicon dioxide, Ge, GaAs, InP, InAs, AlAs, GaN, InN, GaInN, GaAlAs, InSb, fused silica, sapphire, quartz, glass, and BK7.
 41. The grating of claim 37, wherein said first groove material comprises one of crystalline ditantalum pentoxide, polycrystalline ditantalum pentoxide, crystalline hafnium oxide and polycrystalline hafnium oxide.
 42. The grating of claim 37, wherein said dielectric constant is at least
 14. 43. The grating of claim 37, wherein said dielectric constant is at least
 10. 44. A light storage device comprising the grating of claim
 40. 45. A grating for enhancing transmission of a predetermined polarization state of incident electromagnetic radiation at a predetermined wavelength, comprising: a grating structure adapted to support cavity modes that enhance transmission of said predetermined polarization state at said predetermined wavelength, said grating structure comprising: a first layer comprising a first grating structure; a second layer comprising a second grating structure; and a dielectric layer between said first and second layers; said first grating structure having a first period and being associated with a plurality of identical first grooves between a first pair of adjacent wires, each said first period comprising one of said first grooves, each said first groove comprising a first groove height, a first groove width, and a first dielectric constant greater than or equal to 1; and said second grating structure having a second period and being associated with a plurality of identical second grooves between a second pair of adjacent wires, each said second period comprising one of said second grooves, each said second groove comprising a second groove height, a second groove width, and a second dielectric constant greater than or equal to
 1. 46. The grating of claim 45, wherein said first grating structure is further associated with a plurality of identical third grooves between a third pair of adjacent wires, each said first period comprising one of said first grooves and one of said third grooves, each said third groove comprising a third groove height, a third groove width, and a third groove dielectric constant equal to or greater than
 1. 47. The grating of claim 45, further comprising a substrate on which said grating structure is superposed, wherein said substrate comprises one of silica, silicon, silicon dioxide, Ge, GaAs, InP, InAs, AlAs, GaN, InN, GaInN, GaAlAs, InSb, fused silica, sapphire, quartz, glass, and BK7.
 48. The grating of claim 45, further adapted to support cavity modes in adjacent grooves having overlapping transmission spectra, thereby producing light circulation for a normal angle of incidence of said incident electromagnetic radiation and light weaving for a non-normal angle of incidence of said incident electromagnetic radiation.
 49. The grating of claim 45, further adapted to localize said predetermined polarization state of incident electromagnetic radiation at said predetermined wavelength within said grating.
 50. The grating of claim 45, wherein said dielectric layer comprises one or more layers, each said one or more layers comprising at least one of crystalline silicon, poly-crystalline silicon, amorphous silicon, silicon oxide, silicon nitride, gallium arsenide, aluminum arsenide, gallium aluminum arsenide, indium phosphide, indium antimonide, indium phosphide antimonide, gallium nitride, indium nitride, gallium indium nitride, silica, borosilicate glass, mercury cadmium telluride, cadmium sulfide, cadmium telluride, a semiconductor material, an oxide, a polymer and plastic.
 51. The grating of claim 50, wherein each said one or more layers has a thickness of between 5 nm and 400 mm.
 52. A method of fabricating a waveband filter, said waveband filter including a grating structure adapted to enhance transmission of both transverse magnetic (TM) and transverse electric (TE) polarized incident electromagnetic radiation within a waveband that includes a predetermined wavelength, and a substrate on which said grating structure is superposed, said grating structure including a groove dielectric constant ∈_(groove), a grating period Λ, a groove width, and a groove height, said method comprising the steps: selecting said substrate with an index of refraction n_(s) and said grating period Λ such that a first order diffraction occurs at a wavelength λ equal to Λ/n_(s) that is less than said predetermined wavelength; selecting an initial value for said groove width, said groove height and said groove dielectric constant that produce a transmission curve for each of said TM and said TE polarized radiation that at least partially falls within said waveband; iteratively varying a value for said groove height from said initial value and determining a wavelength of a transmission intensity maximum of said TM-polarization state at the iterative values for said groove height to determine an optimal groove height for enhancing transmission of said TM-polarization state at said predetermined wavelength; for said optimal groove height and said initial value of said groove dielectric constant, vary a value for said groove width from said initial value until a transmission intensity maximum of said TE-polarization state is aligned with said transmission intensity maximum of said TM-polarization state at said predetermined wavelength to obtain an optimal groove width; and fabricating said grating structure having said initial value of groove dielectric constant ∈_(groove), said optimal groove height, and said optimal groove width on said substrate.
 53. The method of claim 52, further comprising determining an aspect ratio defined as groove height divided by groove width and varying said aspect ratio, groove height and groove width to adjust a width of said waveband and to align said TM- and TE-polarization transmission curves to said predetermined wavelength. 